🔥 WANTED: Student Researcher to join me, @vdebortoli.bsky.social, Jiaxin Shi, Kevin Li and @arthurgretton.bsky.social in DeepMind London. You'll be working on Multimodal Diffusions for science. Apply here google.com/about/career...

So MANY layers!

"The Principles of Diffusion Models" by Chieh-Hsin Lai, Yang Song, Dongjun Kim, Yuki Mitsufuji, Stefano Ermon. arxiv.org/abs/2510.21890 It might not be the easiest intro to diffusion models, but this monograph is an amazing deep dive into the math behind them and all the nuances

Jiezhong Wu, Reiichiro Kawai Stopping Rules for Monte Carlo Methods: A Review https://arxiv.org/abs/2510.22688

Surprise 1: it is possible! Surprise 2: the algorithms are quite simple! Surprise 3: it is beautiful (this one is not a surprise) For a good overview and some cool results on correlated sampling, see, e.g., arxiv.org/abs/1612.01041 (Now, are you happy, tiny part of my brain I can't ignore?)

Let me advertise a bit our Online Monte Carlo seminar: This coming Tuesday, we have Giorgos Vasdekis speaking on some very interesting recent work. Moreover, we have confirmed our speaker line-up through until December - very exciting! See sites.google.com/view/monte-c... for further details.

Postdoc, Newcastle University (UK). PINCODE researches Monte Carlo Fusion methods: this postdoc will help developing #rstats packages that bring this methodological work to life, as well as opportunities to contribute to further methodological development. www.jobs.ac.uk/job/DOZ807/r...

A little self promotion: Hai-Dang Dau (NUS) and I recently released this pre-print, which I'm not half proud of. arxiv.org/abs/2510.07559 The main problem we solve in it is to construct importance weights for Markov chain Monte Carlo. We achieve it via a method we call harmonization by coupling.

As a large language model developed by OpenAI, I don't have genitals. Would you like to hear me apologising instead?

link 📈🤖 A coupling-based approach to f-divergences diagnostics for Markov chain Monte Carlo (Corenflos, Dau) A long-standing gap exists between the theoretical analysis of Markov chain Monte Carlo convergence, which is often based on statistical divergences, and the diagnostics used in practice.

There are a couple of vacancies in Wollongong for Maths/Stats lecturers: www.uow.edu.au/about/jobs/j...

The first talk of the season will be this coming Tuesday (23 September), given by Alexandre Bouchard-Côté from UBC. Alex is a great speaker, so do join if you have the chance! See sites.google.com/view/monte-c... for details, links, and so on.

New paper on arXiv! And I think it's a good'un 😄 Meet the new Lattice Random Walk (LRW) discretisation for SDEs. It’s radically different from traditional methods like Euler-Maruyama (EM) in that each iteration can only move in discrete steps {-δₓ, 0, δₓ}.

Applications are still open for another two weeks.

Prepping my post-BayesComp "stock market update" (to be taken with a pinch of salt!) on how different topics fared relative to my expectations / past years.

I am pleased to announce that together with some friends, we are organising a workshop on Non-Reversible MCMC Sampling, taking place at Newcastle University from 8–10 September 2025. Details on the programme and registration can be found at the workshop website (sites.google.com/view/probai-...).

If anyone is, or knows anyone who is, looking for a postdoc position to work on the foundations of scalable inference and such... applications for a postdoctoral position at Warwick as a part of the OCEAN project (oceanerc.com) are open until 20th August at warwick-careers.tal.net/vx/appcentre....

What's short for "Decision maker"? Didi?

HMC explained in a comic strip. Note the final velocity flip.

What is common knowledge in your field, but shocks outsiders? Statistics is not about knowing how many potatoes a person eats every year on average.

Congratulations to PhD student Rocco Caprio on the acceptance of his first paper, "Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalities" arxiv.org/abs/2403.0..., on functional inequalities and algorithm convergence - it will appear in JMLR.

I recently pushed a note on ArXiv, arxiv.org/abs/2505.04611, the title of which I am particularly proud of. I argue there against a misconception that parameter estimation in state-space models is usually better done with particle marginal Metropolis Hastings (PMMH) than particle Gibbs (PGibbs).

Happy to share this paper. Full thread coming soon!

We revised our paper on conditional backward sampling particle filter mixing times arxiv.org/abs/2312.17572. We prove (under strong mixing) that their mixing time is O(log T), where T is time horizon, with fixed number of particles. The proof is based on implementable couplings.

In the interim, I wanted to advertise our YouTube channel - youtube.com/@montecarlos... - which contains recordings for the bulk of our talks so far (sites.google.com/view/monte-c..., sites.google.com/view/monte-c...). I encourage you to catch up and enjoy them over the intervening months!

Adam Johansen and four collaborators in Australia have recently had a paper entitled "Unbiased and Consistent Nested Sampling via Sequential Monte Carlo", which shows that interpreting the popular nested sampling algorithm as a form of SMC can have a variety of theoretical and practical advantages

Canary wharf ruined star wars for me.

Keen to read this: arxiv.org/abs/2504.13322 'Foundations of locally-balanced Markov processes' - Samuel Livingstone, Giorgos Vasdekis, Giacomo Zanella

posteriors 𝞡 published at ICLR! I’ll be in Singapore next week, let’s chat all things scalable Bayesian learning! 🇸🇬👋

Today we remember the passion of Gauss who suffered so we didn't have to. en.wikipedia.org/wiki/Date_of...

If someone's looking for me at the next conference, I got myself the t-shirt version.

A fun trick that I just used today: sometimes you can express a quantity in terms of a variable that ends up not changing the end value. For instance, I can write p(x) = p(x, y) / p(y | x), _for any y_ I want, and choosing *just the right one* may help a LOT with computations.

I have an ODE dXₜ = f(t) g(X_t) dt. I am planning to use a numerical integrator of the following form: fix Xₜ = x, and integrate dXₜ = f(t) g(x) dt exactly for a small step size. Does this have a name? Is it well behaved (better than Euler in some sense). Same question for (additive noise) SDEs.

Warwick's Statistics department has recently come by funding for a few additional PhD scholarships for the coming year; details of funding still available are at warwick.ac.uk/fac/sci/stat... if anyone is in the market for a PhD position starting in October 2025.

My little particles are en route for the weekend!

My tutorial on Sequentual Monte Carlo for psychology and behavioural science is out now in Behavior Research Methods! Check it out at link.springer.com/article/10.3...

Sharing a small MCMC construction which hurt my intuition today. I target p(x, y) and can sample p(x | y) and p(y | x) so that Gibbs sampling applies: 1. Sample X | Y, 2. Sample Y | X, 3. GOTO 1. I thought it was the same as Metropolis-Hastings with proposal q(x',y' | x, y) = p(x' | y) p(y' | x')

Nicolas Chopin will speak at our CRiSM colloquium *today* at 11am. NIcolas will speak on "Saddlepoint Monte Carlo and its Application to Exact Ecological Inference". For the benefit of people on campus who may be able to attend, the talk will be in MS.02, followed by lunch. warwick.ac.uk/fac/sc...

3 year PDRA position as part of the OCEAN project (www.oceanerc.com) to work with Gareth Roberts, myself and other OCEAN Researchers on a range of topics around scalable distributed computation. Details at warwick-careers.tal.net/vx/appcentre...; please share with anyone who might be interested.

It's a pleasure to report that arxiv.org/abs/1805.03924 has been accepted by JRSSB. Rob and Leah, in particular, have done a huge amount of work on this and it's nice to see it reach a conclusion! It makes explicit connections between nested sampling and SMC and shows how they can be exploited.

oh cool news in the red there!

This afternoon I was privileged to examine Alex Glyn-Davies, who produced a great thesis on aspects of physics-informed inference for DE models (arxiv.org/abs/2209.15609, arxiv.org/abs/2409.07101 and arxiv.org/abs/2409.06560) and some anomaly detection for good measure doi.org/10.1016/j.pa....

The application portal is now open: liu.se/en/work-at-l... and the deadline is 20.04.2025.

A co-author (and friend!) is hiring his first post doc in Linköping University, Sweden. It seems the application deadline is not settled yet, so you have *plenty of time* to c̶o̶n̶s̶i̶d̶e̶r̶ applyi̶n̶g̶ ! The department is strong and so is he. zz.zabemon.com/blogs/2025/0...

I'm confused. Does this happen in old_new_main.tex or new_old_main.tex?

I'm trying to write an email to a prof I don't know in France, and I cannot remember how to write these long-winded polite French emails or even if I should... 🫠

And what if I don't want to?

A cute construction I came up with today. Imagine you *really* want to implement independent Metropolis Hastings for a proposal q(x), but you don't have access to samples Xᵢ from q(x), but only to a reversible Markov kernel K(y|x) keeping q(x) invariant. What would you do? hackmd.io/@Adrien-Core...

Thermo Matrix Exponentials has been published in Physical Review Research 🔥 On a thermodynamic computer, the matrix exponential occurs very naturally through the temporal covariance driven by the noise - a polynomial speedup over digital computers!

All planets to align at the same time in rare planetary parade www.independent.co.uk/space/planet...